Differentiate the following functions with respect to x:

x³ e^x

Let, y = x³ e^x

We have to find dy/dx

As we can observe that y is a product of two functions say u and v where,

u = x³ and v = e^x

∴ y = uv

As we know that to find the derivative of product of two function we apply product rule of differentiation.

By product rule, we have –

…equation 1

As, u = x³

∴ …equation 2 {∵ }

As, v = e^x

…equation 3 {∵ }

∴ from equation 1, we can find dy/dx

∴

⇒ {using equation 2 & 3}

Hence,